Kinetic Friction Question?

Question

A crate rests on a flatbed truck which is initially traveling at 13.7 m/s on a level road. The driver applies the brakes and the truck is brought to a halt in a distance of 36.2 m. If the deceleration of the truck is constant, what is the minimum coefficient of friction between the crate and the truck that is required to keep the crate from sliding?

Answer 1

The force applied due to braking is
F=ma and equal to the force of friction f
we have to find a
V=at
t= sqrt(2S/a)
V= a sqrt(2S/a)=sqrt(2Sa)
a= V^2/(2S)
f=uN=F and since N=mg
finally
umg=ma
u= a/g= V^2/(2Sg)
u=(13.7)^2/(2 x 36.2 x 9.81)=0.264